Natural Inflation: the status after WMAP 3-year data

Abstract

The model of Natural Inflation is examined in light of recent 3-year data from the Wilkinson Microwave Anisotropy Probe and shown to provide a good fit. The inflaton potential is naturally flat due to shift symmetries, and in the simplest version takes the form $V(\varphi )={\Lambda }^4[1\pm \cos (N\varphi /f)]$. The model agrees with WMAP3 measurements as long as $f>0.7m_{Pl}$ (where $m_{Pl}=1.22\times 10^{19}$GeV) and $\Lambda \sim m_{GUT}$. The running of the scalar spectral index is shown to be small -- an order of magnitude below the sensitivity of WMAP3. The location of the field in the potential when perturbations on observable scales are produced is examined; for $f>5m_{Pl}$, the relevant part of the potential is indistinguishable from a quadratic, yet has the advantage that the required flatness is well-motivated. Depending on the value of $f$, the model falls into the large field ($f\ge 1.5m_{Pl}$) or small field ($f<1.5m_{Pl}$) classification scheme that has been applied to inflation models. Natural inflation provides a good fit to WMAP3 data.

To appear in the proceedings of From Quantum to Cosmos: Fundamental Physics Research in Space, Washington, D.C., 22-24 May 2006

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